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Objective: Howard Rachlin wrote extensively on how value diminishes in a hyperbolic form, and he contributed to understanding choice processes between different commodities as a molar pattern of behavior. The field of behavioral economic demand has been dominated by exponential decay functions, indicating that decreases in consumption of a commodity are best fit by exponential functions. Because of the success of Rachlin's equation at describing how hyperbolic decay affects the value of a commodity across various factors (e.g., delay, probability, social distance), we attempted to extend his equation to behavioral economic demand data for alcohol and opioids., Method: Rachlin's discounting equation was applied to estimate consumption on alcohol purchase task data and nonhuman drug demand data. We compared results of his equation to the exponentiated demand equation using both a mixed-effects modeling approach and a two-stage approach., Results: Rachlin's equation provided better fits to consumption data than the exponentiated equation for both mixed-effects and two-stage modeling. We also found that traditional demand metrics, such as P max , can be derived analytically when using Rachlin's equation. Certain metrics derived from Rachlin's equation appeared to be related to clinical covariates in ways similar to the exponentiated equation., Conclusions: Rachlin's equation better described demand data than did the exponentiated equation, indicating that demand for a commodity may decrease hyperbolically rather than exponentially. Other benefits of his equation are that it does not have the same pitfalls as the current exponential equations and is relatively straightforward in its conceptualization when applied to demand data. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Behavioral economics has been a fruitful area of research in substance use. Mathematical descriptions of how individuals temporally discount the value of a commodity have been correlated with substance use and mathematical descriptions of drug consumption decreasing as a function of price (i.e., demand) predict maladaptive substance use. While there is a logical assumption that temporal factors affect demand for a drug, little has been done to merge these models. Thus, the purpose of this study was to combine models of discounting and demand, extending Howard Rachlin's work and contributions to novel areas of study. Data from 85 participants from Amazon Mechanical Turk (MTurk) who completed a hypothetical cigarette purchase task that included price of and delay to cigarettes were analyzed. Multilevel modeling was used to determine descriptive accuracy of combined additive and multiplicative models of discounting and demand. Of the discounting models used in conjunction with the exponentiated demand equation, the Rachlin hyperboloid best described the delay dimension of consumption. The multiplicative version of the Rachlin equation applied to both delay and price outperformed other models tested. Therefore, existing models of discounting and demand can be extended to modeling consumption data from complex multidimensional experimental arrangements., (© 2022 Society for the Experimental Analysis of Behavior.)

Delay discounting reflects the rate at which a reward loses its subjective value as a function of delay to that reward. Many models have been proposed to measure delay discounting, and many comparisons have been made among these models. We highlight the two-parameter delay discounting model popularized by Howard Rachlin by demonstrating two key practical features of the Rachlin model. The first feature is flexibility; the Rachlin model fits empirical discounting data closely. Second, when compared with other available two-parameter discounting models, the Rachlin model has the advantage that unique best estimates for parameters are easy to obtain across a wide variety of potential discounting patterns. We focus this work on this second feature in the context of maximum likelihood, showing the relative ease with which the Rachlin model can be utilized compared with the extreme care that must be used with other models for discounting data, focusing on two illustrative cases that pass checks for data validity. Both of these features are demonstrated via a reanalysis of discounting data the authors have previously used for model selection purposes., (© 2022 The Authors. Journal of the Experimental Analysis of Behavior published by Wiley Periodicals LLC on behalf of Society for the Experimental Analysis of Behavior.)

Statistical inference (including interval estimation and model selection) is increasingly used in the analysis of behavioral data. As with many other fields, statistical approaches for these analyses traditionally use classical (i.e., frequentist) methods. Interpreting classical intervals and p-values correctly can be burdensome and counterintuitive. By contrast, Bayesian methods treat data, parameters, and hypotheses as random quantities and use rules of conditional probability to produce direct probabilistic statements about models and parameters given observed study data. In this work, we reanalyze two data sets using Bayesian procedures. We precede the analyses with an overview of the Bayesian paradigm. The first study reanalyzes data from a recent study of controls, heavy smokers, and individuals with alcohol and/or cocaine substance use disorder, and focuses on Bayesian hypothesis testing for covariates and interval estimation for discounting rates among various substance use disorder profiles. The second example analyzes hypothetical environmental delay-discounting data. This example focuses on using historical data to establish prior distributions for parameters while allowing subjective expert opinion to govern the prior distribution on model preference. We review the subjective nature of specifying Bayesian prior distributions but also review established methods to standardize the generation of priors and remove subjective influence while still taking advantage of the interpretive advantages of Bayesian analyses. We present the Bayesian approach as an alternative paradigm for statistical inference and discuss its strengths and weaknesses., (© 2019 Society for the Experimental Analysis of Behavior.)

Neurocognitive dysfunctions are frequently identified in the addictions. These dysfunctions may indicate either diffuse dysfunction or may represent separate facets that have differential importance to the addiction phenotype. In a sample (n = 260) of alcohol and/or stimulant users and controls we measured responses across 7 diverse neurocognitive measures. These measures were Continuous Performance, Delay Discounting, Iowa Gambling, Stroop, Tower, Wisconsin Card Sorting, and Letter Number Sequencing. Comparisons were then made between the drug-dependent groups and controls using analysis of variance and also using a machine learning approach to classify participants based on task performance as substance-dependent or controls in 1 tree and as alcohol and/or stimulant users or controls in a second tree. The analysis of variance showed significant differences between groups on the Delay Discounting (p < .001), Iowa Gambling (p < .001), Letter Number Sequencing (p < .001), and Wisconsin Card Sorting (p < .05) tasks. The first classification tree correctly classified between substance-dependent or controls for 88.3% of participants and classified between alcohol and/or stimulant users or controls for 63.9% of participants. Delay discounting was the first split in both trees and in the substance-dependent and control tree. The analysis of variance results largely replicate previous findings. The machine learning classification tree analysis provides evidence to support the hypothesis that different measures of neurocognitive dysfunction represent different processes. Among them, delay discounting was the most robust in categorizing drug dependence. (PsycINFO Database Record, ((c) 2017 APA, all rights reserved).)

Original, open-source computer software was developed and validated against established delay discounting methods in the literature. The software executed approximate Bayesian model selection methods from user-supplied temporal discounting data and computed the effective delay 50 (ED50) from the best performing model. Software was custom-designed to enable behavior analysts to conveniently apply recent statistical methods to temporal discounting data with the aid of a graphical user interface (GUI). The results of independent validation of the approximate Bayesian model selection methods indicated that the program provided results identical to that of the original source paper and its methods. Monte Carlo simulation (n = 50,000) confirmed that true model was selected most often in each setting. Simulation code and data for this study were posted to an online repository for use by other researchers. The model selection approach was applied to three existing delay discounting data sets from the literature in addition to the data from the source paper. Comparisons of model selected ED50 were consistent with traditional indices of discounting. Conceptual issues related to the development and use of computer software by behavior analysts and the opportunities afforded by free and open-sourced software are discussed and a review of possible expansions of this software are provided., (© 2017 Society for the Experimental Analysis of Behavior.)

Insufficient resources are associated with negative consequences including decreased valuation of future reinforcers. To determine if these effects result from scarcity, we examined the consequences of acute, abrupt changes in resource availability on delay discounting-the subjective devaluation of rewards as delay to receipt increases. In the current study, 599 individuals recruited from Amazon Mechanical Turk read a narrative of a sudden change (positive, neutral, or negative) to one's hypothetical future income and completed a delay discounting task examining future and past monetary gains and losses. The effects of the explicit zero procedure, a framing manipulation, was also examined. Negative income shock significantly increased discounting rates for gains and loses occurring both in the future and the past. Positive income windfalls significantly decreased discounting to a lesser extent. The framing procedure significantly reduced discounting under all conditions. Negative income shocks may result in short-term choices., Competing Interests: The authors have declared that no competing interests exist.

Steep discounting of delayed rewards is linked with a variety of unhealthy behaviors that contribute to the major causes of preventable death and disease. Growing evidence suggests that decreases in delay discounting contribute to healthier preferences. This study sought to provide preliminary evidence for the viability of developing a brief priming task to reduce delay discounting in a large, diverse group of individuals. Participants (n=1,122) were randomized to one of three conditions: Future Focus (FF), Present Focus (PF), and Non-Temporal Focus (NTF) intended respectively to decrease, increase, or have no effect on delay discounting. Participants then completed the Monetary Choice Questionnaire, a brief assessment of delay discounting rate. Participants randomized to FF exhibited significantly lower discounting rates than those randomized to PF or NTF conditions. Race, Hispanic background, social self-monitoring, education, and cigarette smoking also accounted for a significant amount of variance in the discounting model. These findings provide support for the development of a brief priming intervention that might be examined in clinical or public health contexts to decrease discounting and support healthy choices., (Copyright © 2016 Elsevier B.V. All rights reserved.)

Ninety-four smokers completed the delay discounting procedure for either hypothetical amounts of money, $10 (money) and $1000 (money) or hypothetical amounts of cigarettes ($10 and $1000 worth of cigarettes). We investigated how variables previously found to be related to rates of delay discounting accounted for the observed results. These variables included the following: demographic information, smoking characteristics, executive function abilities, impulsivity, time perception, and the Utility Measure of Cigarette Reinforcing Efficacy (UMCE). Education level and UMCE were each significantly correlated with 3 out of 4 of the discounting measures. Moreover, the largest effect sizes observed were between these two measures and the four discounting measures. All potential discounting predictors were also investigated using step-wise linear regression with Bayesian Information Criterion (BIC) analysis—these BIC models revealed that education level and UMCE accounted for large portions of the variance. We conclude that education level and UMCE were the most consistent predictors of discounting. This data is discussed within the framework of a widely accepted neuroeconomic model that suggests that two brain systems separately assess two separate facets of decision-making, and the interplay between these two systems determines self-control in smokers. We hypothesize that education level and UMCE may serve as surrogate measures of the functionality of these two systems and that discounting may be a sentinel measure of self-control., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

The study of delay discounting, or valuation of future rewards as a function of delay, has contributed to understanding the behavioral economics of addiction. Accurate characterization of discounting can be furthered by statistical model selection given that many functions have been proposed to measure future valuation of rewards. The present study provides a convenient Bayesian model selection algorithm that selects the most probable discounting model among a set of candidate models chosen by the researcher. The approach assigns the most probable model for each individual subject. Importantly, effective delay 50 (ED50) functions as a suitable unifying measure that is computable for and comparable between a number of popular functions, including both one- and two-parameter models. The combined model selection/ED50 approach is illustrated using empirical discounting data collected from a sample of 111 undergraduate students with models proposed by Laibson (1997); Mazur (1987); Myerson & Green (1995); Rachlin (2006); and Samuelson (1937). Computer simulation suggests that the proposed Bayesian model selection approach outperforms the single model approach when data truly arise from multiple models. When a single model underlies all participant data, the simulation suggests that the proposed approach fares no worse than the single model approach., (© Society for the Experimental Analysis of Behavior.)

Ninety-four smokers completed the delay discounting procedure for either hypothetical amounts of money, $10 (money) and $1000 (money) or hypothetical amounts of cigarettes ($10 and $1000 worth of cigarettes). We investigated how variables previously found to be related to rates of delay discounting accounted for the observed results. These variables included the following: demographic information, smoking characteristics, executive function abilities, impulsivity, time perception, and the Utility Measure of Cigarette Reinforcing Efficacy (UMCE). Education level and UMCE were each significantly correlated with 3 out of 4 of the discounting measures. Moreover, the largest effect sizes observed were between these two measures and the four discounting measures. All potential discounting predictors were also investigated using step-wise linear regression with Bayesian Information Criterion (BIC) analysis — these BIC models revealed that education level and UMCE accounted for large portions of the variance. We conclude that education level and UMCE were the most consistent predictors of discounting. This data is discussed within the framework of a widely accepted neuroeconomic model that suggests that two brain systems separately assess two separate facets of decision-making, and the interplay between these two systems determines self-control in smokers. We hypothesize that education level and UMCE may serve as surrogate measures of the functionality of these two systems and that discounting may be a sentinel measure of self-control. [ABSTRACT FROM AUTHOR]

Abstract: Although the extensive lines of research on delay and/or probability discounting have greatly expanded our understanding of human decision-making processes, the relation between these two phenomena remains unclear. For example, some studies have reported robust associations between delay and probability discounting, whereas others have failed to demonstrate a consistent relation between the two. The current study sought to clarify this relation by examining the relation between delay and probability discounting in a large sample of internet users (n =904) using the Amazon Mechanical Turk (AMT) crowdsourcing service. Because AMT is a novel data collection platform, the findings were validated through the replication of a number of previously established relations (e.g., relations between delay discounting and cigarette smoking status). A small but highly significant positive correlation between delay and probability discounting rates was obtained, and principal component analysis suggested that two (rather than one) components were preferable to account for the variance in both delay and probability discounting. Taken together, these findings suggest that delay and probability discounting may be related, but are not manifestations of a single construct (e.g., impulsivity). [Copyright &y& Elsevier]